The Liar paradox arises via considering the Liar sentence:
L: L is not true.
and then reasoning in accordance with the:
T-schema:
“Φ is true if and only if what Φ says is the case.”
Along similar lines, we obtain the Montague paradox (or the “paradox of the knower“) by considering the following sentence:
M: M is not knowable.
and then reasoning in accordance with the following two claims:
Factivity:
“If Φ is knowable then what Φ says is the case.”
Necessitation:
“If Φ is a theorem (i.e. is provable), then Φ is knowable.”
Put in very informal terms, these results show that our intuitive accounts of truth and of knowledge are inconsistent. Much work in logic has been carried out in attempting to formulate weaker accounts of truth and of knowledge that (i) are strong enough to allow these notions to do substantial work, and (ii) are not susceptible to these paradoxes (and related paradoxes, such as Curry and Yablo versions of both of the. . .